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arXiv 2106.02563cond-mat.mes-hall
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滑动双层石墨烯中的电子能带交叉:紧束缚计算和对称群表示分析

Electronic band crossing in sliding bilayer graphene: Tight-binding calculations and symmetry group representation analysis

V. Nam Do

摘要:

狄拉克点被发现出现,由于在双层石墨烯的电子结构中的带的交叉的配置,其中两个六边形晶格之间的对齐保持两层之间的扶手椅/锯齿形线的平行。基于紧束缚模型对$π$能带的电子计算结果表明,能带色散曲线的交叉发生在六角布里渊区的角点附近。群表示论分析证实了这种狄拉克点的出现。证明了在一般$\mathbf{k}$点处的带交叉是由布里渊区中高对称性$\mathbf{k}$点处本征态对称性之间的相容关系保证的。狄拉克点的存在决定了能面的几何性质,从而决定了费米能面和能谱的拓扑结构。

英文摘要:

Dirac points are found to emerge due to the crossing of bands in the electronic structure of bilayer graphene for configurations in which the alignment between two hexagonal lattices preserves the parallelism of the armchair/zigzag lines between two layers. On the base of electronic calculations using a tight-binding model for the $π$ bands it is shown that the crossing of the energy-band dispersion curves occurs in the vicinity of the corner points of the hexagonal Brillouin zone. Group representation theory analysis confirms the emergence of such Dirac points. It is demonstrated that the band crossings at generic $\mathbf{k}$ points are guaranteed by the compatibility relations between the symmetries of eigenstates at the high-symmetry $\mathbf{k}$ points in the Brillouin zone. The presence of Dirac points governs the geometrical properties of the energy surfaces, and thus the topological structure of the Fermi energy surface and the energy spectrum.

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